Question

A ball is thrown from a height of 67 meters with an initial downward velocity of 5/ms . The ball's height h (in meters) after t seconds is given by the following h=67-5t-5t^2. How long after the ball is thrown does it hit the ground?

Answer 1

3.19459 seconds
Since we've been given the equation for how high the ball is at t seconds, all we need to do is solve for a height of 0. So h = 67 - 5t - 5t^2 0 = 67 - 5t - 5t^2 And you should immediately notice that we have a quadratic equation with A = -5, B = -5, and C=67. Use the quadratic formula to determine the roots of -4.19459 and 3.19459. Since we can't have negative seconds, that means that the ball will hit the ground 3.19459 seconds after it was thrown.